A Unsupervised Framework for Identifying Diverse Quantum Phase Transitions Using Classical Shadow Tomography

Abstract

We provide a general machine learning methodology that integrates classical shadow representations with unsupervised principal component analysis (PCA) to explore various quantum phase transitions. By sampling spin configurations from random Pauli measurements, our approach can effectively analyze hidden statistical patterns in the data, thereby capturing the distinct signatures of quantum criticality through their fluctuations. We benchmark this approach across various spin-1/2 systems, including the 1D XZX cluster-Ising model, the 1D bond-alternating XXZ model, the 2D transverse-field Ising model, and the 2D Kitaev honeycomb model. We show that PCA not only reliably detects and distinguishes both symmetry-breaking and topological transitions, but also enables their qualitative classification based on characteristic fluctuation patterns. Our data-driven approach does not require any knowledge of the Hamiltonian or explicit order parameters, and can therefore be a general and applicable tool for probing new quantum phases.

References in corpus (39)

• Anyons in an exactly solved model and beyond
• Quantum Spin Liquids
• Quantum Spin Liquid States
• Machine learning phases of matter
• Predicting Many Properties of a Quantum System from Very Few Measurements
• The ITensor Software Library for Tensor Network Calculations
• Learning phase transitions by confusion
• Discovering Phase Transitions with Unsupervised Learning
• Probing entanglement entropy via randomized measurements
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• Machine learning quantum phases of matter beyond the fermion sign problem
• Identifying topological order through unsupervised machine learning
• Machine Learning Phases of Strongly Correlated Fermions
• Provably efficient machine learning for quantum many-body problems
• Identifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data
• Unsupervised machine learning and band topology
• Unsupervised machine learning account of magnetic transitions in the Hubbard model
• Machine learning of phase transitions in the percolation and XY models
• Discriminative Cooperative Networks for Detecting Phase Transitions
• Probing scrambling using statistical correlations between randomized measurements
• Machine learning of quantum phase transitions
• Unveiling phase transitions with machine learning
• Many-body topological invariants from randomized measurements
• Unsupervised machine learning of topological phase transitions from experimental data
• Machine-Learning Studies on Spin Models
• Pivot Hamiltonians as generators of symmetry and entanglement
• Machine Learning as a universal tool for quantitative investigations of phase transition
• Unsupervised learning universal critical behavior via the intrinsic dimension
• Divergence of predictive model output as indication of phase transitions
• Unsupervised learning of topological phase transitions using Calinski-Harabaz index
• Deep Learning on the 2-Dimensional Ising Model to Extract the Crossover Region with a Variational Autoencoder
• Intrinsic dimension of path integrals: data mining quantum criticality and emergent simplicity
• Entanglement convertibility by sweeping through the quantum phases of the alternating bonds $XXZ$ chain
• Machine learning on quantum experimental data toward solving quantum many-body problems
• Unsupervised learning of phase transitions via modified anomaly detection with autoencoders
• Unsupervised Interpretable Learning of Phases From Many-Qubit Systems
• Finite Temperature Entanglement Negativity of Fermionic Symmetry Protected Topological Phases and Quantum Critical Points in One Dimension
• Robust Identification of Topological Phase Transition by Self-Supervised Machine Learning Approach
• Self-Supervised Ensemble Learning: A Universal Method for Phase Transition Classification of Many-Body Systems